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A099480 Count from 1, repeating 2n five times. 4
1, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 7, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 13, 14, 14, 14, 14, 14, 15, 16, 16, 16, 16, 16, 17, 18, 18, 18, 18, 18, 19, 20, 20, 20, 20, 20, 21, 22, 22, 22, 22, 22, 23, 24, 24, 24, 24, 24, 25, 26, 26, 26, 26, 26 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Could be called the Jones sequence of the knot 9_43, since the g.f. is the reciprocal of (a parameterization of) the Jones polynomial for 9_43.

Half the domination number of the knight's graph on a 2 X (n+1) chessboard. - David Nacin, May 28 2017

LINKS

Table of n, a(n) for n=0..77.

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-1).

FORMULA

G.f.: 1/((1-x+x^2)(1-x-x^3+x^4)) = 1/(1-2x+2x^2-2x^3+2x^4-2x^5+x^6);

a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-2*a(n-4)+2*a(n-5)-a(n-6), n>5;

a(n) = -cos(Pi*2n/3+Pi/3)/6+sqrt(3)*sin(Pi*2n/3+Pi/3)/18-sqrt(3)*cos(Pi*n/3+Pi/6)/6+sin(Pi*n/3+Pi/6)/2+(n+3)/3.

a(n) = Sum_{i=0..n+1} floor((i-1)/6) - floor((i-3)/6). - Wesley Ivan Hurt, Sep 08 2015

a(n) = A287393(n+1)/2. - David Nacin, May 28 2017

MATHEMATICA

LinearRecurrence[{2, -2, 2, -2, 2, -1}, {1, 2, 2, 2, 2, 2}, 100] (* Vincenzo Librandi, Sep 09 2'15 *)

PROG

(MAGMA) I:=[1, 2, 2, 2, 2, 2]; [n le 6 select I[n] else 2*Self(n-1)-2*Self(n-2)+2*Self(n-3)-2*Self(n-4)+2*Self(n-5)-Self(n-6): n in [1..100]]; // Vincenzo Librandi, Sep 09 2015

CROSSREFS

Cf. A099479, A287393.

Sequence in context: A329097 A197054 A120502 * A025783 A025780 A199121

Adjacent sequences:  A099477 A099478 A099479 * A099481 A099482 A099483

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 18 2004

STATUS

approved

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Last modified November 21 01:33 EST 2019. Contains 329349 sequences. (Running on oeis4.)